Stability in the restricted problem of three bodies with Liapounov Characteristic Numbers

Details Stability in the restricted problem of three bodies with Liapounov Characteristic Numbers Stability in the restricted problem of three bodies with Liapounov Characteristic Numbers

May 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..30...85j&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 30, May 1983, p. 85-95.

Mathematics

7

Dynamic Stability, Liapunov Functions, Orbit Perturbation, Three Body Problem, Computerized Simulation, Constants, Exponents, Matrices (Mathematics)

Scientific paper

The Liapunov Characteristic Numbers (LCNs) method is presently applied to the planar restricted three-body problem, with various mass ratios and Jacobi constants as required by several different cases of satellite and asteroidal motion. LCN results for both ordinary and regularized coordinate systems indicate that a maximum Jacobi constant exists, depending on the mass ratio, such that all LCNs are zero, within computational accuracy, when the Jacobi constant value is greater than the stipulated maximum value. As a consequence, all orbits whose initial conditions are located in the region for which the Jacobi constant is greater than the maximum are effectively stable.

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